Gunsotsu, don't worry about the cropping. Hell, I have to crop even with my 400mm lens:
Rebel XT. EF 400mm f/5.6L USM.
f/5.6. 1/560s. ISO 400. Tripod & tripod collar. mirror-lockup. timer.
I highly recommend playing with a tripod, timer, and mirror-lockup functions for this, and going for a faster shutter speed to eliminate camera shake. Even though you're shooting at night, remember that the moon is a bright sunlit object--you can probably go with a higher shutter speed, lower iso, and smaller aperture than you think.
Also, if you're not using a super-sharp L zoom, I'd recommend stopping down to f/8, and backing off a little from the extreme end of the range, to get the best sharpness you can out of your lens. It did wonders when I used my old 75-300.